A 156 Yes, this is an explicit rule.
There is a rule that defines starting a grapple as an attack -- that is, an iterative attack that you can make more than once as part of a full attack action if you qualify. The rule appears here.
Starting a grapple requires a successful melee attack roll. If you get multiple attacks, you can attempt to start a grapple multiple times (at successively lower base attack bonuses).
A 157 No, there is no explicit rule, but it's probably implied that you can make a grapple attack as an attack of opportunity.
The rules say explicitly only this: An attack of opportunity is a single mêlée attack.
But the rules also imply that some special attacks are mêlée attacks. This is true of the disarm attack, the grapple attack, the sunder attack, and the trip attack.
Other special attacks are not mêlée attacks. The aid another attack is a standard action, the charge attack is a full-round action, the feint attack is a standard action, the overrun attack is a standard action that you take during a standard move, and turning or rebuking undead is a standard action.
The bull rush attack is confusingly called "a standard action (an attack)." A strong reason why you can't make a bull rush attack as an attack of opportunity is that a bull rush always requires you to move at least five feet, which you can't do as part of an attack of opportunity.